Lower bounds for several online variants of bin packing

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201

Scale Dependent Dimension of Luminous Matter in the Universe

We present a geometrical model of the distribution of luminous matter in the universe, derived from a very simple reaction-diffusion model of turbulent phenomena. The apparent dimension of luminous matter, $D(l)$, depends linearly on the logarithm of the scale $l$ under which the universe is viewed: $D(l) \sim 3\log(l/l_0)/\log(\xi/l_0)$, where $\xi$ is a correlation length. Comparison with data from the SARS red-shift catalogue, and the LEDA database provides a good fit with a correlation length $\xi \sim 300$ Mpc. The geometrical interpretation is clear: At small distances, the universe is zero-dimensional and point-like. At distances of the order of 1 Mpc the dimension is unity, indicating a filamentary, string-like structure; when viewed at larger scales it gradually becomes 2-dimensional wall-like, and finally, at and beyond the correlation length, it becomes uniform.Comment: 6 pages, 2 figure

Vector Bin Packing with Multiple-Choice

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types, each with its own cost and $D$-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about $\ln D$ times the optimum. For the running time to be polynomial we require $D=O(1)$ and $T=O(\log n)$. This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin

Radiation Hardness of Thin Low Gain Avalanche Detectors

Low Gain Avalanche Detectors (LGAD) are based on a n++-p+-p-p++ structure where an appropriate doping of the multiplication layer (p+) leads to high enough electric fields for impact ionization. Gain factors of few tens in charge significantly improve the resolution of timing measurements, particularly for thin detectors, where the timing performance was shown to be limited by Landau fluctuations. The main obstacle for their operation is the decrease of gain with irradiation, attributed to effective acceptor removal in the gain layer. Sets of thin sensors were produced by two different producers on different substrates, with different gain layer doping profiles and thicknesses (45, 50 and 80 um). Their performance in terms of gain/collected charge and leakage current was compared before and after irradiation with neutrons and pions up to the equivalent fluences of 5e15 cm-2. Transient Current Technique and charge collection measurements with LHC speed electronics were employed to characterize the detectors. The thin LGAD sensors were shown to perform much better than sensors of standard thickness (~300 um) and offer larger charge collection with respect to detectors without gain layer for fluences <2e15 cm-2. Larger initial gain prolongs the beneficial performance of LGADs. Pions were found to be more damaging than neutrons at the same equivalent fluence, while no significant difference was found between different producers. At very high fluences and bias voltages the gain appears due to deep acceptors in the bulk, hence also in thin standard detectors

Subtle competition between ferromagnetic and antiferromagnetic order in a Mn(II) - free radical ferrimagnetic chain

The macroscopic magnetic characterization of the Mn(II) - nitronyl nitroxide free radical chain (Mn(hfac)2(R)-3MLNN) evidenced its transition from a 1-dimensional behavior of ferrimagnetic chains to a 3-dimensional ferromagnetic long range order below 3 K. Neutron diffraction experiments, performed on a single crystal around the transition temperature, led to a different conclusion : the magnetic Bragg reflections detected below 3 K correspond to a canted antiferromagnet where the magnetic moments are mainly oriented along the chain axis. Surprisingly in the context of other compounds in this family of magnets, the interchain coupling is antiferromagnetic. This state is shown to be very fragile since a ferromagnetic interchain arrangement is recovered in a weak magnetic field. This peculiar behavior might be explained by the competition between dipolar interaction, shown to be responsible for the antiferromagnetic long range order below 3 K, and exchange interaction, the balance between these interactions being driven by the strong intrachain spin correlations. More generally, this study underlines the need, in this kind of molecular compounds, to go beyond macroscopic magnetization measurements.Comment: 12 pages, 10 figures, submitted to Phys. Rev.

Measurement of Galactic Logarithmic Spiral Arm Pitch Angle Using Two-Dimensional Fast Fourier Transform Decomposition

A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.Comment: 23 pages, 22 figures, and 3 Tables; published in ApJS 199, 33 http://iopscience.iop.org/0067-0049/199/2/33/; software available for download at http://dafix.uark.edu/~ages/downloads.html and http://astro.host.ualr.edu/2DFFT

A possible hadronic excess in psi(2S) decay and rho-pi puzzle

We examine the so-called rho-pi puzzle of the psi(2S) decay by incorporating two inputs: One is the relative phase between the one-photon and the gluon decay amplitude, and the other is a possible anomaly in the inclusive nonelectromagnetic decay rate of psi(2S). We propose the possibility that in the psi(2S) decay a hadronic decay process of long distance origin is important in addition to the short-distance decay process. The amplitude of this additional process should nearly cancel the three-gluon amplitude in the exclusive psi(2S)---> 1-0- and turn the sum dominantly real in contrast to the J/psi decay. We present general consequences of this mechanism and then briefly look into two models which possibly explain the course of this additional amplitude.Comment: 14 pages, 2 Tables, and 3 eps figures. Replaces the original version with a minor change in the title and inclusion of more references. The version to appear in Phys. Rev.

Radiation Campaign of HPK Prototype LGAD sensors for the High-Granularity Timing Detector (HGTD)

We report on the results of a radiation campaign with neutrons and protons of Low Gain Avalanche Detectors (LGAD) produced by Hamamatsu (HPK) as prototypes for the High-Granularity Timing Detector (HGTD) in ATLAS. Sensors with an active thickness of 50~$\mu$m were irradiated in steps of roughly 2$\times$ up to a fluence of $3\times10^{15}~\mathrm{n_{eq}cm^{-2}}$. As a function of the fluence, the collected charge and time resolution of the irradiated sensors will be reported for operation at $-30^{\circ}$